shrive555 wrote:
The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum of all the digits of the integers from 0 to 99 inclusive?
A. 450
B. 810
C. 900
D. 1000
E. 1100
Many of the over-mentioned require a good number sense, which I do not posses, so I'll show you my "
layman"
approachWe want the sum of the digits from 0 to 99, so I approximated:
0-9 ->
45 -> (9+0)*10/2
40-49 ->
85 (13+4)*10/2
90-99 ->
135 (18+9)*10/2
We can see at a glance that the "weight" goes up as the numbers go up (meaning the difference between 85 and 45 is 40, while 135-85 is 50, this means that the second part of this sequence carries more weight for our result), so we know that the final answer has to be more than 850 (85*10) but close to it, and that's just 900:
the answer is C.Kudos if you like.Den.